As we find no evidence for the decay \(B^0 \rightarrow X(3872) \gamma \) , we give an upper limit on the branching fraction at 90% confidence level (C.L.).
We apply the Feldman-Cousins counting method [1]} using the implementation provided in the TRolke package [2]}, which takes into account separately the uncertainties in the background and the efficiency.
The expected number of background events \(N_\text{bkg}\)  in the signal region is estimated using the sideband data and the ratio of number of events in the signal region and in the sideband region in the background MC.
The uncertainties in the background levels are studied by comparing the sideband data and the sideband background MC, and are 10.9% and 17.3% for the dimuon and the dielectron channels, respectively.
We thus determine the upper limit on the product of the branching fractions \(\mathcal {B}(B^0 \rightarrow X(3872) \gamma )\times \mathcal {B}(X(3872) \rightarrow J/\psi \pi ^+ \pi ^-)\)  to be \(5.1\times 10^{-7}\)  at the 90% C.L.
The results are summarized in Table REF .
